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 Amaury Pouly

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Average citations per article0.71
Citation Count5
Publication count7
Publication years2011-2017
Available for download3
Average downloads per article62.33
Downloads (cumulative)187
Downloads (12 Months)126
Downloads (6 Weeks)30
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1 published by ACM
October 2017 Journal of the ACM (JACM): Volume 64 Issue 6, November 2017
Publisher: ACM
Citation Count: 0
Downloads (6 Weeks): 26,   Downloads (12 Months): 89,   Downloads (Overall): 89

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The outcomes of this article are twofold. Implicit complexity. We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class P of languages computable in polynomial time in terms of differential equations with polynomial right-hand side. This result gives a purely continuous ...
Keywords: computable analysis, continuous-time models of computation, Analog models of computation, computational complexity, ordinary differential equations, implicit complexity

October 2016 Journal of Complexity: Volume 36 Issue C, October 2016
Publisher: Academic Press, Inc.
Citation Count: 0

In 1941, Claude Shannon introduced the General Purpose Analog Computer (GPAC) as a mathematical model of Differential Analysers, that is to say as a model of continuous-time analog (mechanical, and later on electronic) machines of that time.Following Shannon's arguments, functions generated by the GPAC must satisfy a polynomial differential algebraic ...
Keywords: General Purpose Analog Computer, Analog computation, Continuous-time computations, Real computations

3 published by ACM
July 2016 LICS '16: Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science
Publisher: ACM
Citation Count: 0
Downloads (6 Weeks): 4,   Downloads (12 Months): 31,   Downloads (Overall): 43

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We consider a continuous analogue of (Babai et al. 1996)'s and (Cai et al. 2000)'s problem of solving multiplicative matrix equations. Given k + 1 square matrices A1, ..., Ak, C, all of the same dimension, whose entries are real algebraic, we examine the problem of deciding whether there exist ...
Keywords: hybrid automata, matrix logarithms, exponential matrices, commuting matrices, matrix reachability

May 2016 Theoretical Computer Science: Volume 626 Issue C, May 2016
Publisher: Elsevier Science Publishers Ltd.
Citation Count: 0

In this paper we investigate the computational complexity of solving ordinary differential equations (ODEs) y ' = p ( y ) over unbounded time domains, where p is a vector of polynomials. Contrarily to the bounded (compact) time case, this problem has not been well-studied, apparently due to the "intuition" ...
Keywords: Adaptive Taylor algorithms, Computation with real numbers, Ordinary differential equations, Computational complexity

November 2015 MACIS 2015: Revised Selected Papers of the 6th International Conference on Mathematical Aspects of Computer and Information Sciences - Volume 9582
Publisher: Springer-Verlag New York, Inc.
Citation Count: 0

In this abstract we present a rigorous numerical algorithm which solves initial-value problems IVPs defined with polynomial differential equations i.e.﾿IVPs of the type $$y'=pt,y$$, $$yt_0=y_0$$, where p is a vector of polynomials for any value of t. The inputs of the algorithm are the data defining the initial-value problem, the ...

6 published by ACM
July 2012 ISSAC '12: Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Publisher: ACM
Citation Count: 0
Downloads (6 Weeks): 0,   Downloads (12 Months): 6,   Downloads (Overall): 55

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In this paper we prove that computing the solution of an initial-value problem y = p ( y ) with initial condition y ( t 0 ) = y 0 ∈ R d at time t 0 + T with precision 2 −μ where p is a vector of polynomials ...

August 2011 MFCS'11: Proceedings of the 36th international conference on Mathematical foundations of computer science
Publisher: Springer-Verlag
Citation Count: 2

In this paper we consider the computational complexity of solving initial-value problems defined with analytic ordinary differential equations (ODEs) over unbounded domains of R n and C n , under the Computable Analysis setting. We show that the solution can be computed in polynomial time over its maximal interval of ...

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